Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Lee, J.-H., Tanaka, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209455
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials / J.-H. Lee, H. Tanaka // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 37 назв. — англ.

Let Γ be a dual polar graph with diameter D⩾3, having as vertices the maximal isotropic subspaces of a finite-dimensional vector space over the finite field Fq equipped with a non-degenerate form (alternating, quadratic, or Hermitian) with Witt index D. From a pair of a vertex x of Γ and a maximal c...